Computer generated sequences for downlink and uplink signals in wireless communication systems

ABSTRACT

The present disclosure provides a base station transmitter, a user equipment transmitter and methods of operating the base station and user equipment transmitters. In one embodiment, the base station transmitter is for use with a cellular communication system and includes a synchronization unit configured to provide a randomly-generated constant amplitude zero autocorrelation (random-CAZAC) sequence corresponding to a downlink synchronization signal. Additionally, the base station transmitter also includes a transmit unit configured to transmit the downlink synchronization signal using the random-CAZAC sequence. In another embodiment, the user equipment transmitter is for use with a cellular communication system and includes a reference signal unit configured to provide a random-CAZAC sequence for an uplink reference signal corresponding to a one resource block allocation of the user equipment. The user equipment transmitter also includes a transmit unit configured to transmit the uplink reference signal using the random-CAZAC sequence.

CROSS-REFERENCE TO PROVISIONAL APPLICATION

This application claims the benefit of U.S. Provisional Application No.60/913,743 entitled “New Design of Constant Amplitude ZeroAuto-correlation (CAZAC) Sequences for Communication Systems” to AnandG. Dabak and Eko N. Onggosanusi filed on Apr. 24, 2007, which isincorporated herein by reference in its entirety.

This application also claims the benefit of U.S. Provisional ApplicationNo. 60/914,216 entitled “Design of Length 12 UL-RS for LTE Using RandomConstant Amplitude Zero Auto-Correlation (CAZAC) Sequences” to Anand G.Dabak and Aris Papasakellariou filed on Apr. 26, 2007, which isincorporated herein by reference in its entirety.

This application additionally claims the benefit of U.S. ProvisionalApplication No. 60/970,311 entitled “Design of CAZAC Sequences for SmallRB Allocations in E-UTRA UL” to Anand G. Dabak and Aria Papasakellarioufiled on Sep. 6, 2007, which is incorporated herein by reference in itsentirety.

This application further claims the benefit of U.S. ProvisionalApplication No. 60/971,470 entitled “Design of CAZAC Sequences for SmallRB Allocations in E-UTRA UL (Update)” to Anand G. Dabak and ArisPapasakellariou filed on Sep. 11, 2007, which is incorporated herein byreference in its entirety.

TECHNICAL FIELD

The present disclosure is directed, in general, to a cellularcommunication system and, more specifically, to a base stationtransmitter, a user equipment transmitter and methods of operating thesame.

BACKGROUND

In a cellular communication network, each cell employs a base stationthat communicates with user equipment, such as a laptop, a PDA or a cellphone that is actively located within its cell. When the user equipmentis first turned on, it performs an initial cell search in order to beconnected to the cellular network. This involves a downlinksynchronization process between the base station and the user equipmentwherein the base station sends a synchronization signal to the userequipment.

Based on channel quality indications perceived by the user equipment,communication resource blocks associated with the cellular network maybe allocated to the user equipment. The number of resource blocks thatare allocated depends somewhat on the number of users within the celland the ability of their equipment to accommodate a larger number ofresource blocks. The ability of the user equipment to accommodate alarger number of resource blocks improves data rates and reduces cellplanning constraints. Since cellular communication systems offer greatflexibility in their use, improvements would prove beneficial in theart.

SUMMARY

Embodiments of the present disclosure provide a base stationtransmitter, a user equipment transmitter and methods of operating thebase station and user equipment transmitters. In one embodiment, thebase station transmitter is for use with a cellular communication systemand includes a synchronization unit configured to provide arandomly-generated constant amplitude zero autocorrelation(random-CAZAC) sequence corresponding to a downlink synchronizationsignal. Additionally, the base station transmitter also includes atransmit unit configured to transmit the downlink synchronization signalusing the random- CPZAC sequence.

In another embodiment, the user equipment transmitter is for use with acellular communication system and includes a reference signal unitconfigured to provide a randomly-generated constant amplitude zeroautocorrelation (random-CAZAC) sequence for an uplink reference signalcorresponding to a one resource block allocation of the user equipment.Additionally, the user equipment transmitter also includes a transmitunit configured to transmit the uplink reference signal using therandom-CAZAC sequence.

In yet another embodiment, the user equipment transmitter is for usewith a cellular communication system and includes a reference signalunit configured to provide a QPSK sequence for an uplink referencesignal corresponding to a one or two resource block allocation of theuser equipment. Additionally, the user equipment transmitter alsoincludes a Zadoff-Chu sequence unit configured to generate s Zadoff-Chusequence for the uplink reference signal corresponding to a resourceblock allocation of three or more for the user equipment. The userequipment transmitter further includes a transmit unit configured totransmit the uplink reference signal.

In another aspect, the present disclosure provides a method of operatinga base station transmitter for use with a cellular communication system.The method includes providing a randomly-generated constant amplitudezero autocorrelation (random-CAZAC) sequence corresponding to a downlinksynchronization signal. The method also includes transmitting thedownlink synchronization signal using the random-CAZAC sequence.

The present disclosure also provides a method of operating a userequipment transmitter for use with a cellular communication system. Themethod includes providing a randomly-generated constant amplitude zeroautocorrelation (random-CAZAC) sequence for an uplink reference signalcorresponding to a one resource block allocation of the user equipments.The method also includes transmitting the uplink reference signal usingthe random-CAZAC sequence.

The present disclosure further provides another method of operating auser equipment transmitter for use with a cellular communication system.The method includes providing a QPSK sequence for an uplink referencesignal corresponding to a one or two resource block allocation of theuser equipment. The method also includes generating a Zadoff-Chusequence for the uplink reference signal corresponding to a resourceblock allocation of three or more for the user equipment. The methodfurther includes transmitting the uplink reference signal.

The foregoing has outlined preferred and alternative features of thepresent disclosure so that those skilled in the art may betterunderstand the detailed description of the disclosure that follows.Additional features of the disclosure will be described hereinafter thatform the subject of the claims of the disclosure. Those skilled in theart will appreciate that they can readily use the disclosed conceptionand specific embodiment as a basis for designing or modifying otherstructures for carrying out the same purposes of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present disclosure, referenceis now made to the following descriptions taken in conjunction with theaccompanying drawings, in which:

FIGS. 1A and 1B illustrate embodiments of a cellular network constructedaccording to the principles of the present disclosure;

FIG. 2 illustrates a typical maximum periodic correlation for anembodiment of 128 random-CAZAC sequences of length 64 constructed,according to the principles of the present disclosure;

FIGS. 3A and 3B illustrate examples of ripple in the time and frequencydomains, respectively;

FIGS. 4A and 4B illustrate periodic autocorrelations of 32 respectiverandom-CAZAC sequences wherein each of the codes shown have a zeroautocorrelation;

FIG. 5 illustrates cumulative distribution functions ofcross-correlations for random-CAZAC sequences and extended or truncatedZadoff-Chu sequences;

FIGS. 6A and 6B illustrate bit error rate comparisons for random-CAZACsequences and extended Zadoff-Chu sequences;

FIG. 7 illustrates a bit error rate comparison between a random-CAZACsequence and a Zadoff-Chu sequence in the presence of AWGN interference;

FIGS. 8A and 8B illustrate cumulative distribution functions ofcross-correlations of the Random CAZAC sequences with themselves andwith extended Zadoff-Chu (E-ZC) sequences of length three RBs;

FIG. 9 illustrates cumulative distribution functions of all cyclic shiftcross-correlations for QPSK sequence of length 12 with itself, with ofextended DC sequences of length 36 and of extended ZC of length 12 with36;

FIG. 10 illustrates the cubic metric of the QPSK sequence of length 12sequences;

FIG. 11 illustrates a flow diagram of an embodiment of a method ofoperating a base station transmitter carried out according to theprinciples of the present disclosure;

FIG. 12 illustrates a flow diagram of an embodiment of a method ofoperating a user equipment transmitter carried out according to theprinciples of the present disclosure; and

FIG. 13 illustrates a flow diagram of another embodiment of a method, ofoperating a user equipment transmitter carried out according to theprinciples of the present disclosure,

DETAILED DESCRIPTION

Constant amplitude zero auto correlation (CAZAC) sequences are veryimportant in cellular communication systems because they facilitate thetiming detection of a signal. The constant amplitude (CA) propertyensures appropriate power amplifier efficiency and the zeroauto-correlation (ZAC) property ensures that the correct timing isdetected. Further the ZAC property is also important in equalization ofcommunication systems because the channel estimate that is obtained fromthe sequence has a flat spectrum in the frequency domain.

Zadoff-Chu sequences are typical of CAZAC sequences that are currentlyemployed in cellular communication systems for first-stage downlinksynchronization. However one of the problems with employing theZadoff-Chu sequence in this role is that it exhibits a time-frequencyambiguity or uncertainty.

The time-frequency ambiguity may also be understood by looking at theZadoff-Chu sequence

${{S(n)} = ^{({j\frac{\pi \; {Mn}^{2}}{N}})}},$

where n is time, N is the length of the sequence and M is the sequencenumber. Now consider a timing error δ in the code position

$\begin{matrix}{{S\left( {n - \delta} \right)} = {^{({j\frac{\pi \; {M{({n - \delta})}}^{2}}{N}})} = {^{({j\frac{\pi}{N}{M{({n^{2} = {{2n\; \delta} + \delta^{2}}})}}})}.}}} & (1)\end{matrix}$

Similarly, consider a frequency error Ω in the code

$\begin{matrix}{{{^{{- j}\; 2{\pi\Omega}\; n}{S(n)}} = ^{({j{({\frac{\pi \; {Mn}^{2}}{N} - {2\Omega \; n}})}})}},} & (2)\end{matrix}$

where

${\Omega = \frac{\Delta \; f}{f_{samp}}},$

Δf is the frequency estimation error in Hz and f_(samp) is the samplingfrequency in Hz. For a first stage acquisition in a 3GPP LTE system, forexample, the f_(samp) is 1.96 Msamples/second. Comparing equations (1)and (2), it may be seen that the timing error in code position detectionimplies an equivalent frequency error of

$\begin{matrix}{\frac{2\pi \; M\; \delta \; n}{N} = {\left. {2{\pi\Omega}\; n}\Rightarrow{\Delta \; f} \right. = {\frac{M\; \delta \; f_{samp}}{N}.}}} & (3)\end{matrix}$

If the first stage of LTE acquisition is run with a correlator at 2×sampling of the input signal, then for worst case

$\delta = \frac{1}{2}$

and f_(samp)=1.96e6, N=64, M=1, the worst case frequency offset error isgiven by 15.3 kHz. For a 5 ppm crystal at center frequency of 2 GHz, themaximum frequency offset can be plus or minus 10 kHz. This implies thatif there is small timing error detection in the first stage of a primarysynchronization code (PSC) detection, the estimated frequency error canbe more than that expected from the crystal offset. Hence, making afrequency correction in the first stage of acquisition may actually bemore detrimental than helpful to a receiver operating in thisenvironment.

A major constraint in the current E-UTRA design is the number of CAZACsequences for small resource block (RB) allocations. Particularly forthe case of one RB, the structure of an uplink reference signal (UL-RS)was changed from two short blocks to one long block per slot in order toaccommodate a maximum of 12 instead of six CAZAC sequences. However,critical issues remain.

Truncating a length 13 Zadoff-Chu sequence can result in 12 CAZACsequences wherein six of the sequences have a cubic metric (CM)substantially larger that QPSK by as much as 1.15 dB. This is a seriousproblem particularly for the ACK/NAK and possibly for channel qualityindication (CQI) transmissions that rely entirely on the transmission ofCAZAC sequences.

Cyclic extension of a length 11 ZC sequence provides better CMproperties than truncation, although four of the 10 resulting sequencesstill have CM up to 0.3 dB greater that QPSK. However, communicationcell planning or possible sequence hopping is further inhibited by thesmaller number (10) of total sequences.

Cell or base station planning in E-UTRA for the allocation of 10 or 12CAZAC sequences seems necessary as sequence hopping results in arelative large collision probability due to the small number of totalsequences employing either extension or truncation. The small number ofsequences imposes the need for tighter planning.

The issues discussed above become even more serious in the case ofACK/NAK and possibly CQI signaling due to the slow BER requirements(especially for the NAK) and the use of all cyclic shifts within thesame cell. Then, in order to distinguish ACK/NAK transmission from userequipments (UEs) near the border of two cells of the same Node B,different CAZAC sequences are likely required.

Considering that only 10 or 12 such sequences are available (with onlysix having CM less that QPSK) and that planning is already challengingeven with Node B specific sequences, it becomes apparent that havingcell specific sequences is an extremely difficult challenge particularlyif the Node Bs have a variable number and non-perfectly shaped cells.Moreover, as the CM for some of the sequences is larger than QPSK,coverage is limited by the ACK/NAK and not by the data transmission ofone RB, which has a much larger target BER due to the potential of verylow coding rate (e.g., for 10 percent BLER and HARQ).

To overcome these limitations, embodiments of the present disclosureemploy randomly-generated CAZAC sequences (herein denoted asrandom-CAZAC sequences) or computer generated QPSK sequences that do notexhibit this time-frequency ambiguity or uncertainty and allow a largernumber of sequences to be provided.

FIGS. 1A and 1B illustrate embodiments of a cellular communicationnetwork, generally designated 100 and 150, constructed according to theprinciples of the present disclosure. In FIG. 1A, the cellularcommunication network 100 shows a diagram of an embodiment wherein abase station (Node B) employs a base station transmitter 105 to providea downlink synchronization signal to user equipment (UE). The basestation transmitter 105 includes a synchronization unit 106 and atransmit unit 107 to provide the downlink synchronization signal to theUE.

In the illustrated embodiment, the synchronization unit 106 isconfigured to provide a randomly-generated constant amplitude zeroautocorrelation (random-CAZAC) sequence corresponding to the downlinksynchronization signal. Additionally, the transmit unit 107 isconfigured to transmit the downlink synchronization signal using therandom-CAZAC sequence. In this particular embodiment, the downlinksynchronization signal is a primary synchronization signal.

The random-CAZAC sequences are not chirp-like sequences, such as theZadoff-Chu sequences, and therefore, do not exhibit the time-frequencyambiguity, as noted earlier. Examples of the random-CAZAC sequencesincluded in this disclosure were generated by computer search. Theprocedure for generating the random-CAZAC sequences of length N may bedescribed as follows.

-   (1) Let i=1, in a first step generate N random complex numbers    {tilde over (X)}_(i) ^(f)={{tilde over (x)}_(i) ^(f)(1), {tilde over    (x)}_(i) ^(f)(2), . . . , {tilde over (x)}_(i) ^(f)(n), . . . ,    {tilde over (x)}_(i) ^(f)(N)}.-   (2) Next, define the sequence

$\begin{matrix}{\begin{matrix}{X_{i}^{f} = \left\{ {{x_{i}^{f}(1)},{x_{i}^{f}(2)},\ldots,{x_{i}^{f}(n)},\ldots,{x_{i}^{f}(N)}} \right\}} \\{= \left\{ {\frac{{\overset{\sim}{x}}_{i}^{f}(1)}{\left| {{\overset{\sim}{x}}_{i}^{f}(1)} \right|},\frac{{\overset{\sim}{x}}_{i}^{f}(2)}{\left| {{\overset{\sim}{x}}_{i}^{f}(2)} \right|},\ldots,\frac{{\overset{\sim}{x}}_{i}^{f}(n)}{\left| {{\overset{\sim}{x}}_{i}^{f}(n)} \right|},\cdots,\frac{{\overset{\sim}{x}}_{i}^{f}(N)}{\left| {{\overset{\sim}{x}}_{i}^{f}(N)} \right|}} \right\}}\end{matrix}.} & (4)\end{matrix}$

-   (3) Now, let the sequence {tilde over (X)}_(i) ^(f)={{tilde over    (x)}_(i) ^(f)(1), {tilde over (x)}_(i) ^(f)(2), . . . , {tilde over    (x)}_(i) ^(f)(N)} be the IFFT of sequence X_(i) ^(f). Then, define    the sequence

$\begin{matrix}{\begin{matrix}{X_{i}^{t} = \left\{ {{x_{i}^{t}(1)},{x_{i}^{t}(2)},\ldots,{x_{i}^{t}(n)},\ldots,{x_{i}^{t}(N)}} \right\}} \\{= \left\{ {{Q_{k}\left( \frac{{\overset{\sim}{x}}_{i}^{t}(1)}{\left| {{\overset{\sim}{x}}_{i}^{t}(1)} \right|} \right)},{Q_{k}\left( \frac{{\overset{\sim}{x}}_{i}^{t}(2)}{\left| {{\overset{\sim}{x}}_{i}^{t}(2)} \right|} \right)},\ldots,{Q_{k}\left( \frac{{\overset{\sim}{x}}_{i}^{t}(n)}{\left| {{\overset{\sim}{x}}_{i}^{t}(n)} \right|} \right)},\cdots,{Q_{k}\left( \frac{{\overset{\sim}{x}}_{i}^{t}(N)}{\left| {{\overset{t}{x}}_{i}^{f}(N)} \right|} \right)}} \right\}}\end{matrix},} & (5)\end{matrix}$

where Q_(K)(y);y is a complex scalar number of unit amplitude thatdenotes the quantization of the phase of y to

$\frac{k\; \pi}{K};$

k=0, 1, 2, . . . , K=1 using either a round off, floor or ceilingfunction. As K→∞, no quantization of the phase is done in the limit.This quantization of phase is introduced if one wants to limit theresulting sequence K_(M) ^(t) phases from lying any where on the unitcircle.

-   (4) Let the FFT of the sequence X_(t) ^(f) be now denoted by {tilde    over (X)}_(i) ^(f), set i=i+1 and now go back to step (2). Repeat    the above steps (2), (3) and (4) for say M=1000 or more.

For a large number of iterations where K□ 1, (e.g., for K=4096), theresulting sequence X_(M) ^(t) is a random-CAZAC sequence. Further,several such random-CAZAC sequences can be generated by starting with adifferent random sequence in step (1) above. For finite K, the resultingsequence X_(i) ^(t) still has good autocorrelation properties, howeverthe autocorrelation may not be zero like the actual CAZAC sequence.Conversely it implies that the frequency domain characteristic may notbe exactly flat. For K=16, an approximately 3 dB peak to peak ripple inthe frequency domain may be observed, while for K=32, a 2 dB ripple inthe frequency domain may be observed. Several other interestingproperties of the randomly generated CAZAC sequences (K□ 1) arediscussed below.

Generally, upon convergence and as discussed earlier, theautocorrelation of the generated random-CAZAC sequences is a deltafunction, and it provides constant amplitude elsewhere in the timedomain. Additionally, the frequency domain spectrum is substantiallycompletely flat.

FIG. 2 illustrates a graph 200 showing a typical maximum periodiccorrelation for an embodiment of 128 random-CAZAC sequences of length 64constructed according to the principles of the present disclosure. Thecross correlation properties of different random-CAZAC sequences X_(i)^(t) and for different i are quite good. For N=64, the maximum periodicautocorrelation between the different random-CAZAC sequences is about 18most of the time, while it could go as high as 30 when only 500random-CAZAC sequences are generated.

FIGS. 3A and 3B illustrate graphs 300, 350 showing examples of ripple inthe time and frequency domains, respectively. The ripple may be definedin the time and frequency domains for every step i as

$\begin{matrix}{{r_{i}^{t} = {20*\log \; 10\left( \frac{\max \left( {{abs}\left( {{\overset{\sim}{x}}_{i}^{t}(n)} \right)} \right)}{\min\left( {{abs}\left( {{\overset{\sim}{x}}_{i}^{t}(n)} \right)} \right.} \right)}};{r_{i}^{f} = {20*\log \; 10{\left( \frac{\max \left( {{abs}\left( {{\overset{\sim}{x}}_{i}^{f}(n)} \right)} \right)}{\min \left( {{abs}\left( {{\overset{\sim}{x}}_{i}^{f}(n)} \right)} \right)} \right).}}}} & (6)\end{matrix}$

These may be seen to decrease monotonically in both the time andfrequency domains as the number of iterations increase.

Table 1 enumerates some of the different sequences that have beengenerated for N=64 and for K=16 and K=32 respectively. Since allsequences are constant amplitude, only the phase is shown as a ratio of

$\frac{\pi}{16}\mspace{14mu} {and}\mspace{14mu} \frac{\pi}{32}$

respectively. The codes in columns 1-5 are the codes for K=16, and thosein columns 6-10 are for K=32. For example, the phase value of the firstcode (1) and the first sample 15 corresponds to a phase of

$\frac{15*\pi}{16},$

which represents 168.75 degrees.

TABLE 1${Random}\mspace{14mu} {codes}\mspace{14mu} {for}\mspace{14mu} {phase}\mspace{14mu} {quantization}\mspace{14mu} \frac{\pi}{16}\left( {K = 16} \right)\mspace{14mu} {and}\mspace{14mu} \frac{\pi}{32}\left( {K = 32} \right)$1 2 3 4 5 6 7 8 9 10  1 15 10 2 9 −6 −11 8 10 11 −4  2 −6 −14 −8 12 3−28 −18 −13 18 0  3 −14 −9 5 6 5 29 32 21 11 3  4 −11 14 −2 −6 −5 26 −12−10 16 −16  5 14 −10 −10 −12 5 −31 −9 9 −13 23  6 8 6 8 3 10 14 30 1 319  7 −11 −2 10 3 15 −9 −25 18 4 18  8 1 1 13 −13 −1 −11 −18 20 16 −10 9 4 12 −9 −12 −1 19 3 −27 −25 16 10 −11 −9 −14 8 −12 −12 −2 −23 −24 2611 −5 −4 12 0 6 20 26 −12 13 −16 12 6 2 3 9 −16 −18 −19 −11 −5 31 13 10−3 11 2 3 24 4 28 −5 19 14 13 11 10 −6 1 −16 −25 −26 28 −9 15 3 12 7 2 9−21 6 17 −17 22 16 11 3 −11 −6 10 −5 8 1 −27 0 17 3 3 −13 −6 −13 3 1 −28−3 −30 18 11 −14 14 2 10 12 3 −11 −13 −30 19 14 15 8 9 −8 17 −15 9 −17−26 20 4 13 13 −12 −1 −31 −10 17 8 31 21 2 −2 9 −7 7 −31 −2 8 −2 −20 229 3 −1 −14 4 −18 −16 9 23 −18 23 −7 10 4 −16 −4 20 12 30 5 12 24 −13 2−6 11 7 −24 −9 −16 25 7 25 12 −7 −1 5 14 −32 12 17 17 −6 26 −6 5 7 15 13−28 17 29 23 17 27 12 −2 15 −10 7 10 6 9 −4 16 28 −15 0 −6 14 1 −7 2 −10−8 −6 29 −3 −5 −7 −13 7 −10 −23 19 −26 −18 30 −14 4 12 −16 10 11 −29 300 −7 31 7 −10 −12 6 −5 −24 −8 3 25 −21 32 3 10 1 −7 15 3 27 −10 28 25 33−12 1 −10 16 −6 18 −11 30 28 22 34 5 6 4 −15 3 −18 0 23 12 −24 35 10 1612 0 −5 −6 −23 −22 −31 −13 36 6 −2 −10 −15 −5 11 6 −11 2 −29 37 2 −2 8−6 −12 −21 −23 11 21 −22 38 6 −12 5 −9 −15 31 31 28 12 28 39 −9 −14 −1111 −3 4 −12 7 −23 −15 40 −13 2 9 −3 −4 −21 9 12 19 −11 41 10 14 −8 9 −921 −14 −4 22 −25 42 0 0 15 −11 15 16 −28 11 23 24 43 12 3 −9 −8 −3 9 17−14 17 24 44 −10 6 −10 13 14 −12 −20 −3 −13 −23 45 14 0 −9 −4 −1 −8 1−16 2 9 46 4 9 −14 13 11 19 2 −24 27 17 47 −6 8 5 16 −5 1 10 20 −23 3048 11 −12 16 6 −5 −20 −23 6 −4 −14 49 14 −2 −6 −3 11 −11 30 28 24 22 5010 −11 −2 6 −8 2 30 4 14 −11 51 −7 6 15 −13 1 16 25 −24 −6 29 52 2 −3 13−2 3 −11 −18 −32 27 −16 53 6 1 13 −12 10 −3 −28 30 18 −26 54 4 11 9 9 6−25 25 −26 22 −6 55 −12 −6 −7 14 −8 −32 −1 12 −12 14 56 −15 13 15 12 7−31 7 25 −6 −31 57 −12 8 −12 −11 0 21 15 −25 −22 3 58 −13 1 1 −10 −4 13−30 25 −6 25 59 −4 13 −7 −4 −15 −31 2 −11 −30 −9 60 −1 −5 1 −14 15 −28−4 30 −16 −24 61 −4 −15 15 −9 −12 −8 −1 27 16 13 62 2 −8 14 −1 11 −31 −4−30 9 12 63 −16 −10 −11 3 10 −28 31 −20 −12 16 64 −5 14 −2 9 −1 31 26−31 27 −27

Referring again to FIG. 1A and in the context of an LTE system, threeprimary synchronization sequences (PSCs) are used to facilitate timingacquisition, frequency offset estimation and partial cellidentification. In this case, it is important to keep the UE receivecomplexity small. While three sequences can he used for thisapplication, it is beneficial to exploit inherent properties of CAZACsequences to reduce complexity.

Since the proposed random-CAZAC sequences are complex-valued andstatistically behave similar to pseudo-noise (PN) sequences, it isexpected that the complex conjugate of a particular random CAZACsequence S*(n) has small cross-correlation with the original sequenceS(n). This property can be exploited to generate two sequences from onerandom-CAZAC sequence S(n), which have small cross-correlationproperties. It is apparent that the autocorrelation profile of S(n) andS*(n) are identical. If quantized correlation is used, it is alsoexpected that the profile for S*(n) is similar to S(n). Moreover,exploiting this property will result in a receiver complexity reduction.This is because the correlation between the received signal R(n) withS(n) shares the same terms as that with S*(n). Hence, only onecorrelation computation is needed for the two sequences.

Furthermore, it is also possible to modulate S(n) with some regularphase rotation, for example exp(j*θ*n)S(n), to generate more sequences(where θ is a constant phase shift such as

$\frac{\pi}{2}$

or π). While this extension can generate even more sequences from onerandom-CAZAC sequence with small cross-correlation properties, thecomplexity reduction is minimal, if any, compared to the above complexconjugate extension.

Keeping the above in mind, it is possible to generate three primarysynchronization sequences from two random-CAZAC sequences generated bythe procedure presented above. That is

PSC ₁(n)=S _(i)(n)

PSC ₂(n)=S ₁*(n).   (7)

PSC ₃(n)=S ₂(n)

It is also possible to replace S₂(n) with S₂*(n) for PSC₃(n). The aboveconstruction only requires two correlations as opposed to three, whichresults in a 25 percent reduction in computational complexity.

The three PSCs designed with the above construction are advantageouslydefined in the time domain. That is, the length N PSC sequence ismodulated with a certain waveform (e.g., SRRC, Gaussian, etc.). Thewaveform is intended to define the spectrum characteristic of thesequence and chosen to meet the spectrum mask. After modulating with thewaveform, cyclic prefix is added to emulate an OFDMA symbol. Then, theresulting symbol is time multiplexed with other OFDMA symbols within thedefined sub-frame. Similarly, the DC term is subtracted from the codesin order to ensure a zero term at the DC.

In FIG. 1B, the cellular network 150 shows a diagram of an embodimentwherein user equipment (UE) employs a user equipment transmitter 155 toprovide an uplink reference signal to the Node B. The user equipmenttransmitter 155 includes a reference signal unit 156, a Zadoff-Chusequence unit 157 and a transmit unit 158 to provide the uplinkreference signal to the Node B.

In one embodiment, the reference signal unit 156 is configured toprovide a randomly-generated constant amplitude zero autocorrelation(random-CAZAC) sequence for an uplink reference signal corresponding toa one resource block allocation of the user equipment. Additionally, therandom-CAZAC sequence may be extended to correspond to a two resourceblock allocation of the user equipment. The Zadoff-Chu sequence unit 156is configured to generate the uplink reference signal corresponding to athree or more resource block allocation for the user equipment. Thetransmit unit 158 is configured to transmit the uplink reference signal.

The random-CA AC sequences for one or two RB allocations are generatedemploying the procedure discussed with respect to FIG. 1A above. Morethan 30 such sequences may be obtained for one RB allocation wherein allhave a CM lower than QPSK and mean cross-correlations similar to the oneachieved with just 10 or 12 sequences resulting from the Zadoff-Chuextension or truncation, respectively.

Nevertheless, for greater than three RE allocations where manyZadoff-Chu generated sequences exist satisfying the above properties,Zadoff-Chu extension or truncation may still be used as a specificformula exists for the generation of Zadoff-Chu sequences for the primelength employing simple and singular circuitry for large RB allocations.

FIGS. 4A and 4B illustrate a graph 400 showing periodic autocorrelationsof 32 respective random-CAZAC sequences wherein each of the codes shownhave a zero autocorrelation. Several thousand random-CAZAC codes may befound by starting from the random initialization in step (1) of theprocedure discussed with respect to FIG. 1A. Approximately 30,000random-CAZAC sequences were generated from the above procedure and thensorted according to their CM properties. Additionally, they were sortedaccording to the periodic cross-correlation over the whole sequence.This alleviates a problem where cyclic shifts of the same sequence maybe used by different UEs in a cell or in different cells of the sameNode B. A total of 33 sequences were obtained, which are identified tohave good CM and cross-correlation properties. The CM of these sequencesare lower than the CM of PSK.

Table 2 summarizes the different statistical properties for the UL-RSgenerated using random-CA AC, sequences and those generated usingZadoff-Chu (ZC) sequences. The first two columns show the cyclicperiodic cross-correlation properties. The last three columns show theCM properties.

TABLE 2 Statistics of UL-RS generated with ZC extension or truncationand random-CAZAC sequences. Number of Sequences Square root with CMTotal mean square less than number of Mean cross- cross Mean Min Max orequal to sequences correlation correlation CM CM CM QPSK (1.22) ZCCyclic 10 0.28 0.29 0.85 0.17 1.50 6 Extension ZC Truncation 12 0.270.29 1.37 0.46 2.36 6 Random-CAZAC 10 0.26 0.29 0.46 0.14 0.61 10Sequences 1-10 Random-CAZAC 16 0.26 0.29 0.56 0.14 0.77 16 Sequences1-16 Random-CAZAC 24 0.26 0.29 0.67 0.14 0.95 24 Sequences 1-24Random-CAZAC 33 0.26 0.29 0.78 0.14 1.22 33 Sequences 1-33

As can be seen from Table 2, the ULRS designed using random-CAZACsequences have similar (or slightly smaller) mean cross-correlation andmean square cross-correlation as those designed with ZC sequences havingcyclic extension or truncation. Hence, the performance with an UL-RSdesigned using random-CAZAC sequences is expected to be similar to anUL-RS designed with extended ZC sequences in the presence of inter-NodeB (or inter-cell) interference. In addition, an UL RS designed usingrandom-CAZAC sequences has the advantage of employing a much largernumber of sequences while simultaneously providing a substantially lowerCM.

FIG. 5 illustrates a graph 500 showing cumulative distribution functionsof cross-correlations for random-CAZAC sequences and extended ortruncated Zadoff-Chu sequences. Graph 500 shows a comparison of therandom-CAZAC sequence to a ZC11 sequence extended to 12 and ZC13sequence truncated to 12.

FIGS. 6A and 6B illustrate graphs 600 and 650 showing bit error ratecomparisons for random-CAZAC sequences and extended Zadoff-Chusequences. The graph 600 corresponds to a single interfering UE, and thegraph 650 corresponds to two interfering UEs. The bit error rate (BER)results are for an ACK/NAK transmission with sequence hopping betweentwo slots and flat fading, for maximum impact. For the worst case of asingle dominant interferer, the performance loss from the random CAZACsequence is only 0.35 dB at 0.01% BER. With two equal-power interferers,the loss at 0.01% BER reduces to 0.2 dB. In both cases, the loss isnegligible at higher BERs. In the presence of additional cyclic shifthopping per symbol and orthogonal cover sequence hopping, theinterference is expected to be further randomized implying that the losswill be further reduced as compared to that shown in FIGS. 6A and 6B.

FIG. 7 illustrates a graph 700 showing a bit error rate comparisonbetween a random-CAZAC sequence and a Zadoff-Chu. sequence in thepresence of AWGN interference, Here, the Zadoff-Chu sequence is a ZC11extended to 12. The graph 700 confirms the trend in performance lossreduction from adding interferers stated above with respect to FIGS. 6Aand 6B. No performance difference is observed between the Random CAZACand extended ZC sequences.

Salient advantages of an UL-RS designed using Random-CAZAC sequences maybe summarized as follows. If only 10 UL-RS sequences are needed (as forZC sequences with extension), the worst case CM of the UL-RS employing aRandom-CAZAC sequence is 0.6019 dB, which is substantially lower thanthe CM of ZC extended sequences by 0.67 dB. Further, the largest CM forthe 32 Random-CAZAC sequences is smaller than the QPSK CM of 1.05 dB by0.35 dB.

If the worst case CM of the UL-RS generated with the random-CAZACsequence is set to be equal to that of QPSK (1.05 dB), at least 32 UL-RSsequences can be obtained. This compares with only 10 UL-RS sequencesusing ZC extension. Note that even among these 10 codes, 4 codes have CMgreater than that of QPSK.

Because 32 Random-CAZAC generated UL-RS sequences exist for l RBemploying 12 sub-carriers, random sequence hopping for the UL-RS can bedone for one RB allocations with much smaller probability of collisionswith UL-RS transmitted by a UE in a different cell or the Node B. Sincethere are two UL-RS per sub-frame, the probability of a collision withsequence hopping is

$\left( {\frac{1}{29} \times \frac{1}{29}} \right){0.0012.}$

This compares with probability of

$\left( {\frac{1}{2} \times \frac{1}{2}} \right)0.0069$

with ZC truncated sequences or

$\left( {\frac{1}{10} \times \frac{1}{10}} \right)0.01$

with ZC extended sequences. Therefore, Node B (or cell) planning may beavoided or substantially reduced with random-CAZAC sequences.

Random-CAZAC sequence generation provides full flexibility in tradingoff the number of generated sequences with the largest CM. For example,a number of random-CAZAC sequences larger than 32 may be obtained byallowing for somewhat larger CM and an even lower CM could be obtainedby decreasing the number of random-CAZAC sequences below 32. Theprevious advantages of the 32 Random-CAZAC sequences extend to ACK/NACKsignaling as it also occurs within one RB.

Table 3 summarizes the comparison of UL-RS signal design for one RB oflength 12 using a random CAZAC sequence compared to using an extendedZadoff-Chu of length 12.

TABLE 3 Comparison of UL-RS design with length 12 using Random-CAZAC andextended/truncated ZC Sequences. UL-RS designed using UL-RS designedusing Parameter Random-CAZAC extended ZC of length 11 Number ofSequences 32 10 or 12 Worst case CM 1.21 dB < QPSK 1-50 dB > QPSK (1.22dB) (1.22 dB) or 2.36 dB > QPSK (1.22 dB) Sequence planning Easier(avoided) Harder Mean and mean-square Similar Similar cross correlationSequence hopping for 1 Better Worse RB (UL-RS, ACK/ NACK)

Although the previous analysis focused on allocations of one RB, it canbe extended in the same manner to larger RB allocations. Since the smallRB allocations place a limit on the number of available sequences withgood CM and cross-correlations and on associated cell planning or theeffectiveness of sequence hopping, random-CAZAC sequence generation canapply to allocations of one RB and probably two RBs while the usual ZCsequences can be used for larger RB allocations. Since for allocationsof three RBs, 30 sequences with appropriate CM properties can begenerated with ZC extension, 30 random-CAZAC sequences may be used forone and two RB allocations.

This implies that 30 sequences of length 12 and 30 sequences of length24 need to be stored at the UE for use with one RB and two RBallocations. The sequence generation for larger RB allocations can beaccomplished employing the usual circuitry used for ZC sequencegeneration. Alternately, using random-CAZAC sequences only for one RBallocations allows selection of 22 sequences out of the available 33sequences (for lowest CM or cross-correlations), which is the same with22 sequences available for two RB allocations with cyclic extension.Then, only 22 sequences of length 12 need to be stored.

The random-CAZAC sequences discussed above were given in the timedomain. Table 4 reflects statistics for 30 corresponding frequencydomain code sets or a one RB allocation (length 12) and a two RBallocation (length 24).

TABLE 4 Statistics of ZC extension/truncation and Random CAZACSequences. Square Root Number of Mean Square Sequences Mean Cross-Cross- with CM Correlation Correlation less than Total of all of all orequal Number of Cyclic Cyclic Mean Min to QPSK Sequences Shifts ShiftsCM CM Max CM (1.22) ZC Cyclic 10 0.28 0.29 0.85 0.17 1.50 6 Extension ZC12 0.27 0.29 1.37 0.46 2.36 6 Truncation Length 12 30 0.26 0.29 0.730.14 1.14 30 Random CAZAC Sequences 1-30 Length 24 30 0.18 0.20 0.960.23 1.22 30 Random CAZAC Sequences 1-30As can be seen from Table 4, the 30 Random CAZAC sequences of length 12and 24 have similar or less CM as compared to QPSK (CM=1,22 using a CMslope of 1.56).

FIGS. 8A and 8B illustrate graphs 800 and 850 showing cumulativedistribution functions of cross-correlations of the Random CAZACsequences with themselves and with extended Zadoff-Chu (E-ZC) sequencesof length three RBs. Graph 800 compares the cross correlation of theRandom CAZAC sequences of length 12 against the cross correlation ofthese sequences with Random CAZAC sequences of length 24 and E-ZCsequences of length 36. Similarly, graph 850 compares thecross-correlation of length 24 Random CAZAC sequences among themselvesand against length 36 E-ZC sequences. As seen in FIGS. 8A and 8B, thecumulative distribution functions (CDFs) of the Random CAZAC codes issimilar to their CDF with E-ZC of length 36.

Statistics for the cross-correlation in FIGS. 8A and 8B is given belowin Table 5.

TABLE 5 Statistics for different cross-correlations in FIGS. 8A and 8B(normalized) (Sequence 1, Mean of all Cyclic Shift Mean Square of CyclicSequence 2) Cross-Correlation Shift Cross-Correlation (R-CAZAC length12, 0.27 0.30 E-ZC length 36) (E-ZC length 12, 0.26 0.29 E-ZC length 36)(R-CAZAC length 12, 0.26 0.29 R-CAZAC length 24) (E-ZC length 12, 0.260.29 E-ZC length 24) (R-CAZAC length 24, 0.18 0.20 E-ZC length 36) (E-ZClength 24, 0.18 0.20 E-ZC length 36)As can be seen from Table 5, the statistics of cross-correlation forrandom-CAZAC sequences of length 12 and 24 and that of E-ZC sequences oflength 12 and 24 with sequences of larger RBs are similar to each other.Hence the performance of random-CAZAC sequences for small RBs is similarto extended ZC sequences. The bit error rate comparisons discussed withrespect to FIGS. 6A, 6B and 7 are also valid for these random-CAZACsequences, as well. Assuming six bits of precision to represent thephase of the random-CAZAC sequence, the memory storage for therandom-CAZAC sequences is 297 bytes for length 12 and 594 bytes forlength 24.

Referring again to FIG. 1B and in another embodiment of the userequipment transmitter, the reference signal unit 156 is configured toprovide a QPSK sequence for the uplink reference signal corresponding toa one or two resource block allocation of the user equipment. TheZadoff-Chu sequence unit 157 is configured to generate a Zadoff-Chusequence for the uplink reference signal corresponding to a resourceblock allocation of three or more for the user equipment. The transmitunit is configured to transmit the uplink reference signal to the NodeB.

Table 6 reflects different statistical properties for correspondingfrequency domain code sets for a one RB allocation (length 12) wherein aQPSK structure is provided using compute generated (CG) code.

TABLE 6 Statistics of ZC extension/truncation and CG QPSK length 12Sequences Square Root Number of Mean Square Sequences Mean Cross- Crosswith CM Correlation Correlation less than Total of all of all or equalNumber of Cyclic Cyclic Mean Min Max to QPSK Sequences Shifts Shifts CMCM CM (1.22) ZC Cyclic 10 0.28 0.29 0.85 0.17 1.50 6 Extension ZC 120.27 0.29 1.37 0.46 2.36 6 Truncation Length 12 CG 30 0.26 0.29 0.280.007 0.51 30 Sequences 1-30As evident from Table 6, the 30 CG QPSK sequences of length 12 lower CMas compared to QPSK (CM=1.22 using a CM slope of 1.56). Note that havinga CM lower than QPSK is especially important for one RB allocationssince the PUCCH transmission is entirely based on the transmission ofsuch CAZAC sequences.

FIG. 9 illustrates a graph 900 showing cumulative distribution functionsof all cyclic shift cross-correlations for a CG QPSK sequence of length12 with itself, with of extended ZC sequences of length 36 and ofextended ZC of length 12 with 36. As evident from the graph 900, thecross-correlation CDF of CG QPSK length 12 sequences is similar to thecorresponding CDF with E-ZC of length 36. Statistics for thecross-correlations in FIG. 9 are given below in Table 7.

TABLE 7 Statistics for different cross-correlations in FIGS. 2 and 3(normalized) (Sequence 1, Mean of all Cyclic Shift Mean Square of CyclicSequence 2) Cross-Correlations Shift Cross-correlations (CG length 12,0.26 0.30 E-ZC length 36) (E-ZC length 12, 0.26 0.29 E-ZC length 36)As evident from Table 7, the statistics of cross-correlation for a CGQPSK sequence of length 12 against E-ZC of length 36 is similar to thatof E-ZC of length 12 against E-ZC of length 36. Hence, the performanceof CG length 12 is expected to be similar to that of the extended ZCsequences.

FIG. 10 illustrates a graph 1000 showing the cubic metric of the CG QPSKlength 12 sequences. The CM is seen to increase step-wise with anincrease in code index and maintains an adequate CM. Additionally, thememory storage for storing the sequences is only 720 bits, and henceonly contributes to a small fractional percentage of overall UE memorystorage.

The CG QPSK code stored in the UE memory are shown below:

TABLE 8 The QPSK sequences stored in UE memory are given in the form ofreal and imaginary parts of the sequence. Real value of ComputerGenerated QPSK Sequences Seq (Sample number) No. 1 2 3 4 5 6 7 8 9 10 1112 1 0.707 −0.707 0.707 −0.707 0.707 0.707 −0.707 −0.707 0.707 0.7070.707 0.707 2 0.707 −0.707 0.707 −0.707 −0.707 0.707 0.707 −0.707 −0.707−0.707 −0.707 −0.707 3 0.707 −0.707 −0.707 0.707 0.707 −0.707 0.707−0.707 0.707 0.707 0.707 0.707 4 0.707 −0.707 0.707 −0.707 −0.707 −0.707−0.707 −0.707 0.707 0.707 −0.707 −0.707 5 0.707 −0.707 0.707 0.707−0.707 −0.707 0.707 −0.707 −0.707 −0.707 −0.707 0.707 6 0.707 −0.7070.707 0.707 −0.707 0.707 0.707 0.707 0.707 0.707 0.707 −0.707 7 0.707−0.707 −0.707 0.707 −0.707 0.707 −0.707 0.707 0.707 0.707 −0.707 −0.7078 0.707 −0.707 0.707 −0.707 −0.707 −0.707 0.707 0.707 −0.707 −0.707−0.707 −0.707 9 0.707 −0.707 0.707 −0.707 0.707 −0.707 −0.707 0.7070.707 0.707 0.707 −0.707 10 0.707 −0.707 −0.707 0.707 0.707 0.707 0.7070.707 0.707 −0.707 0.707 0.707 11 0.707 −0.707 −0.707 0.707 0.707 −0.7070.707 0.707 0.707 0.707 0.707 0.707 12 0.707 −0.707 0.707 0.707 −0.707−0.707 −0.707 0.707 0.707 0.707 −0.707 0.707 13 0.707 −0.707 0.707−0.707 0.707 0.707 −0.707 −0.707 0.707 0.707 −0.707 −0.707 14 0.707−0.707 0.707 −0.707 −0.707 0.707 −0.707 0.707 0.707 0.707 0.707 0.707 150.707 −0.707 −0.707 0.707 0.707 −0.707 −0.707 0.707 0.707 0.707 0.7070.707 16 0.707 −0.707 0.707 −0.707 0.707 0.707 0.707 0.707 −0.707 −0.707−0.707 −0.707 17 0.707 −0.707 0.707 0.707 −0.707 0.707 0.707 0.707−0.707 −0.707 −0.707 0.707 18 0.707 −0.707 −0.707 −0.707 0.707 0.7070.707 −0.707 0.707 0.707 −0.707 0.707 19 0.707 −0.707 0.707 −0.707−0.707 0.707 0.707 −0.707 −0.707 0.707 −0.707 0.707 20 0.707 −0.707−0.707 0.707 0.707 0.707 0.707 0.707 0.707 −0.707 −0.707 0.707 21 0.707−0.707 −0.707 0.707 0.707 0.707 0.707 −0.707 0.707 −0.707 0.707 −0.70722 0.707 −0.707 0.707 0.707 −0.707 −0.707 0.707 0.707 0.707 0.707 0.7070.707 23 0.707 −0.707 −0.707 0.707 −0.707 −0.707 −0.707 −0.707 −0.707−0.707 0.707 0.707 24 0.707 −0.707 −0.707 −0.707 0.707 0.707 0.707−0.707 −0.707 0.707 −0.707 0.707 25 0.707 −0.707 −0.707 −0.707 0.707−0.707 −0.707 0.707 −0.707 0.707 0.707 −0.707 26 0.707 −0.707 −0.7070.707 −0.707 0.707 0.707 −0.707 0.707 0.707 0.707 −0.707 27 0.707 −0.7070.707 0.707 0.707 0.707 0.707 0.707 −0.707 −0.707 −0.707 0.707 28 0.707−0.707 −0.707 −0.707 0.707 0.707 0.707 0.707 0.707 0.707 −0.707 0.707 290.707 −0.707 −0.707 −0.707 −0.707 −0.707 0.707 0.707 0.707 −0.707 0.707−0.707 30 0.707 −0.707 0.707 0.707 0.707 −0.707 −0.707 −0.707 −0.707−0.707 0.707 0.707 Imaginary value of Computer Generated QPSK SequencesSeq (Sample number) No. 1 2 3 4 5 6 7 8 9 10 11 12 1 0.707 −0.707 0.707−0.707 0.707 0.707 −0.707 −0.707 0.707 0.707 0.707 0.707 2 0.707 −0.7070.707 −0.707 −0.707 0.707 0.707 −0.707 −0.707 −0.707 −0.707 −0.707 30.707 −0.707 −0.707 0.707 0.707 −0.707 0.707 −0.707 0.707 0.707 0.7070.707 4 0.707 −0.707 0.707 −0.707 −0.707 −0.707 −0.707 −0.707 0.7070.707 −0.707 −0.707 5 0.707 −0.707 0.707 −0.707 −0.707 −0.707 0.7070.707 −0.707 −0.707 −0.707 −0.707 6 0.707 −0.707 −0.707 0.707 −0.7070.707 −0.707 0.707 0.707 0.707 −0.707 −0.707 7 0.707 −0.707 0.707 0.707−0.707 0.707 0.707 0.707 0.707 0.707 0.707 −0.707 8 0.707 −0.707 0.7070.707 −0.707 −0.707 0.707 −0.707 −0.707 −0.707 −0.707 0.707 9 0.707−0.707 −0.707 0.707 0.707 −0.707 0.707 0.707 0.707 0.707 0.707 0.707 100.707 −0.707 0.707 0.707 −0.707 −0.707 −0.707 0.707 0.707 0.707 −0.7070.707 11 0.707 −0.707 0.707 −0.707 0.707 −0.707 −0.707 0.707 0.707 0.7070.707 −0.707 12 0.707 −0.707 −0.707 0.707 0.707 0.707 0.707 0.707 0.707−0.707 0.707 0.707 13 0.707 −0.707 0.707 −0.707 0.707 0.707 0.707 0.707−0.707 −0.707 −0.707 −0.707 14 0.707 −0.707 −0.707 0.707 0.707 −0.707−0.707 0.707 0.707 0.707 0.707 0.707 15 0.707 −0.707 0.707 −0.707 −0.7070.707 −0.707 0.707 0.707 0.707 0.707 0.707 16 0.707 −0.707 0.707 −0.7070.707 0.707 −0.707 −0.707 0.707 0.707 −0.707 −0.707 17 0.707 −0.7070.707 0.707 −0.707 0.707 0.707 0.707 −0.707 −0.707 −0.707 0.707 18 0.707−0.707 −0.707 −0.707 0.707 0.707 0.707 −0.707 0.707 0.707 −0.707 0.70719 0.707 −0.707 −0.707 0.707 0.707 0.707 0.707 0.707 0.707 −0.707 −0.7070.707 20 0.707 −0.707 0.707 −0.707 −0.707 0.707 0.707 −0.707 −0.7070.707 −0.707 0.707 21 0.707 −0.707 −0.707 0.707 −0.707 −0.707 −0.707−0.707 −0.707 −0.707 0.707 0.707 22 0.707 −0.707 −0.707 −0.707 0.7070.707 0.707 −0.707 −0.707 0.707 −0.707 0.707 23 0.707 −0.707 −0.7070.707 0.707 0.707 0.707 −0.707 0.707 −0.707 0.707 −0.707 24 0.707 −0.7070.707 0.707 −0.707 −0.707 0.707 0.707 0.707 0.707 0.707 0.707 25 0.707−0.707 0.707 0.707 0.707 0.707 0.707 0.707 −0.707 −0.707 −0.707 0.707 260.707 −0.707 −0.707 −0.707 0.707 0.707 0.707 0.707 0.707 0.707 −0.7070.707 27 0.707 −0.707 −0.707 −0.707 0.707 −0.707 0.707 0.707 −0.7070.707 0.707 −0.707 28 0.707 −0.707 −0.707 0.707 −0.707 0.707 0.707−0.707 0.707 0.707 0.707 −0.707 29 0.707 0.707 −0.707 −0.707 0.707−0.707 0.707 −0.707 −0.707 0.707 −0.707 −0.707 30 0.707 −0.707 0.707−0.707 −0.707 0.707 −0.707 −0.707 0.707 −0.707 −0.707 −0.707

TABLE 9 The computer generated QPSK sequence codes from Table$8\mspace{14mu} {are}\mspace{14mu} {given}\mspace{14mu} {in}\mspace{14mu} {the}\mspace{14mu} {phase}\mspace{14mu} {quantization}\mspace{14mu} {format}\mspace{14mu} \frac{\pi}{4}\left( {K = 4} \right)\mspace{14mu} {{below}.}$Computer Generated Computer Generated QPSK Sequences Sequence (Samplenumber) Number 1 2 3 4 5 6 7 8 9 10 11 12 1 1 −3 1 −3 1 1 −3 −3 1 1 1 12 1 −3 1 −3 −3 1 1 −3 −3 −3 −3 −3 3 1 −3 −3 1 1 −3 1 −3 1 1 1 1 4 1 −3 1−3 −3 −3 −3 −3 1 1 −3 −3 5 1 −3 1 −1 −3 −3 1 3 −3 −3 −3 −1 6 1 −3 −1 1−3 1 −1 1 1 1 −1 −3 7 1 −3 3 1 −3 1 3 1 1 1 3 −3 8 1 −3 1 3 −3 −3 1 −1−3 −3 −3 3 9 1 −3 −1 3 1 −3 3 1 1 1 1 3 10 1 −3 3 1 −1 −1 −1 1 1 3 −1 111 1 −3 3 −1 1 −3 −1 1 1 1 1 −1 12 1 −3 −1 1 3 3 3 1 1 −1 3 1 13 1 −3 1−3 1 1 3 3 −1 −1 −3 −3 14 1 −3 −1 3 3 −1 −3 1 1 1 1 1 15 1 −3 3 −1 −1 3−3 1 1 1 1 1 16 1 −3 1 −3 1 1 −1 −1 3 3 −3 −3 17 1 −3 1 1 −3 1 1 1 −3 −3−3 1 18 1 −3 −3 −3 1 1 1 −3 1 1 −3 1 19 1 −3 −1 3 3 1 1 3 3 −1 −3 1 20 1−3 3 −1 −1 1 1 −1 −1 3 −3 1 21 1 −3 −3 1 −1 −1 −1 −3 −1 −3 1 3 22 1 −3−1 −1 3 3 1 −1 −1 1 −1 1 23 1 −3 −3 1 3 3 3 −3 3 −3 1 −1 24 1 −3 3 3 −1−1 1 3 3 1 3 1 25 1 −3 3 3 1 3 3 1 −3 −1 −1 3 26 1 −3 −3 −1 3 1 1 3 1 1−1 3 27 1 −3 −1 −1 1 −1 −1 1 −3 3 3 −1 28 1 −3 −3 3 −1 1 1 −1 1 1 3 −129 1 3 −3 −3 3 −3 1 −1 −1 3 −1 −3 30 1 −3 1 −1 −1 3 −3 −3 3 −3 −1 −1

FIG. 11 illustrates a flow diagram of an embodiment of a method ofoperating a base station transmitter 1100 carried out according to theprinciples of the present disclosure. The method 1100 is for use with acellular communication system and starts in a step 1105. Then, in a step1110, a base station transmitter is provided, and a randomly-generatedconstant amplitude zero autocorrelation (random-CAZAC) sequencecorresponding to a downlink synchronization signal is provided in a step1115.

The random CAZAC sequence may be used for a primary synchronizationsequence. Additionally, two complex random CAZAC sequences and one oftheir complex conjugates may be employed to provide three primarysynchronization sequences. The random CAZAC sequence may be provided inthe time domain.

A group of the random CAZAC sequences provides a mean cross-correlationthat is no greater than a corresponding group of cyclic extended ortruncated Zadoff-Chu sequences. Additionally, a group of the randomCAZAC sequences provides a square root mean square cross-correlationthat is no greater than a corresponding group of cyclic extended ortruncated Zadoff-Chu sequences. Correspondingly, a group of the randomCAZAC sequences provides a cubic metric that is no greater than acorresponding group of cyclic extended or truncated Zadoff-Chusequences. The downlink synchronization signal is transmitted using therandom-CAZAC sequence in a step 1120, and the method 1100 ends in a step1125.

FIG. 12 illustrates a flow diagram of an embodiment of a method ofoperating a user equipment transmitter 1200 carried out according to theprinciples of the present disclosure. The method 1200 is for use with acellular communication system and starts in a step 1205. Then, in a step1210, a randomly-generated constant amplitude zero autocorrelation(random-CAZAC) sequence is provided for an uplink reference signalcorresponding to a one resource block allocation of the user equipment.

In one embodiment, the random-CAZAC sequence is extended to correspondto a two resource block allocation of the user equipment. Therandom-CAZAC sequence is selected from a group of random-CAZAC sequencesthat is stored in the user equipment. Additionally, the random-CAZACsequence is provided in the frequency domain.

A group of the random CAZAC sequences provides a mean cross-correlationthat is no greater than a corresponding group of cyclic extended ortruncated Zadoff-Chu sequences. Additionally, the group of random CAZACsequences provides a square root mean square cross-correlation that isno greater than a corresponding group of cyclic extended or truncated.Zadoff-Chu sequences. Correspondingly, the group of random CAZACsequences provides a cubic metric that is no greater than acorresponding group of cyclic extended or truncated Zadoff-Chusequences.

A Zadoff-Chu sequence for the uplink reference signal corresponding to athree or more resource block allocation for the user equipment isprovided in a step 1215. The uplink reference signal is transmitted in astep 1220, and the method 1200 ends in a step 1225.

FIG. 13 illustrates a flow diagram of another embodiment of a method ofoperating a user equipment transmitter 1300 carried out according to theprinciples of the present disclosure. The method 1300 is for use with acellular communication system and starts in a step 1305. Then, in a step1310, a QPSK sequence is provided for an uplink reference signalcorresponding to a one or two resource block allocation of the userequipment. The QPSK sequence is selected from a group of QPSK sequencesthat is stored in the user equipment.

A group of the QPSK sequences provides a mean cross-correlation that nogreater than a corresponding group of cyclic extended or truncated.Zadoff-Chu sequences. Additionally, the group of the QPSK sequencesprovides a square root mean square cross-correlation that is no greaterthan a corresponding group of cyclic extended or truncated Zadoff-Chusequences. Correspondingly, the group of the QPSK sequences provides acubic metric that is no greater than a corresponding group of cyclicextended or truncated Zadoff-Chu sequences.

In one embodiment, the QPSK sequence is selected from the QPSK sequencesconsisting of e^(jφ(n)π/4), where the value of φ(n); n=0, 1, . . . , 11is given by one of the sequences below

S1={1, −3, 3, 1, −1, −1, −1, 1, 1, 3, −1, 1};

S2={1, −3, −1, 3, 3, −1, −3, 1, 1, 1, 1, 1};

-   -   S1={1, −3, 1, 1, −3, 1, 1, 1, −3, −3, −3, 1};    -   S4={1, −3, 3, −1, −1, 1, 1, −1, −1, 3, −3 1};    -   S5={1, −3, 3, 3, 1, 3, 3, 1, −3, −1, −1, 3}; and    -   S6={1, 3, −3, −3, 3, −3, 1, −1, −1, 3, −1, −3}.

A Zadoff-Chu sequence for the uplink reference signal corresponding to aresource block allocation of three or more for the user equipment isgenerated in a step 1315. The uplink reference signal is transmitted ina step 1320, and the method 1300 ends in a step 1325.

While the methods disclosed herein have been described and shown withreference to particular steps performed in a particular order, it willbe understood that these steps may be combined, subdivided, or reorderedto form an equivalent method without departing from the teachings of thepresent disclosure. Accordingly, unless specifically indicated herein,the order or the grouping of the steps is not a limitation of thepresent disclosure.

Those skilled in the art to which the disclosure relates will appreciatethat other and further additions, deletions, substitutions andmodifications may be made to the described example embodiments withoutdeparting from the disclosure.

1-30. (canceled)
 31. A user equipment transmitter for use with acellular communication system, comprising: a reference signal unitconfigured to provide a QPSK sequence for an uplink reference signalcorresponding to a one or two resource block allocation of the userequipment; a Zadoff-Chu sequence unit configured to generate aZadoff-Chu sequence for the uplink reference signal corresponding to aresource block allocation of three or more for the user equipment; and atransmit unit configured to transmit the uplink reference signal. 32.The user equipment transmitter as recited in claim 31 wherein the QPSKsequence is selected from a group of QPSK sequences that is stored inthe user equipment.
 33. The user equipment transmitter as recited inclaim 31 wherein a group of the QPSK sequences provides a meancross-correlation that is no greater than a corresponding group ofcyclic extended or truncated Zadoff-Chu sequences.
 34. The userequipment transmitter as recited in claim 31 wherein a group of the QPSKsequences provides a square root mean square cross-correlation that isno greater than a corresponding group of cyclic extended or truncatedZadoff-Chu sequences.
 35. The user equipment transmitter as recited inclaim 31 wherein a group of the QPSK sequences provides a cubic metricthat is no greater than a corresponding group of cyclic extended ortruncated Zadoff-Chu sequences.
 36. The user equipment transmitter asrecited in claim 31 wherein the QPSK sequence is selected from the QPSKsequences consisting of e^(jφ(n)π/4), where the value of φ(n); n=0, 1, .. . , 11 is given by one of the sequences below: {φ(0), φ(1), . . . ,φ(11)} S1={1, −3, 3, 1, −1, −1, −1, 1, 1, 3, −1, 1}; S2={1, −3, −1, 3,3, −1, −3, 1, 1, 1, 1, 1}; S3={1, −3, 1, 1, −3, 1, 1, 1, −3, −3, −3, 1};S4={1, −3, 3, −1, −1, 1, 1, −1, −1, 3, −3 1}; S5={1, −3, 3, 3, 1, 3, 3,1, −3, −1, −1, 3}; and S6={1, 3, −3, −3, 3, −3, 1, −1, −1, 3, −1, −3}.37. A method of operating a user equipment transmitter for use with acellular communication system, comprising: providing a QPSK sequence foran uplink reference signal corresponding to a one or two resource blockallocation of the user equipment; generating a Zadoff-Chu sequence forthe uplink reference signal corresponding to a resource block allocationof three or more for the user equipment; and transmitting the uplinkreference signal.
 38. The method as recited in claim 37 wherein the QPSKsequence is selected from a group of QPSK sequences that is stored inthe user equipment.
 39. The method as recited in claim 37 wherein agroup of the QPSK sequences provides a mean cross-correlation that is nogreater than a corresponding group of cyclic extended or truncatedZadoff-Chu sequences.
 40. The method as recited in claim 37 wherein agroup of the QPSK sequences provides a square root mean squarecross-correlation that is no greater than a corresponding group ofcyclic extended or truncated Zadoff-Chu sequences.
 41. The method asrecited in claim 37 wherein a group of the QPSK sequences provides acubic metric that is no greater than a corresponding group of cyclicextended or truncated Zadoff-Chu sequences.
 42. The method as recited inclaim 37 wherein the QPSK sequence is selected from the QPSK sequencesconsisting of e^(jφ(n)π/4), where the value of ); n=0, 1, . . . , 11 isgiven by one of the sequences below: {φ(0), φ(1), . . . , φ(11)} S1={1,−3, 3, 1, −1, −1, −1, 1, 1, 3, −1, 1}; S2={1, −3, −1, 3, 3, −1, −3, 1,1, 1, 1, 1}; S3={1, −3, 1, 1, −3, 1, 1, 1, −3, −3, −3, 1}; S4={1, −3, 3,−1, −1, 1, 1, −1, −1, 3, −3 1}; S5={1, −3, 3, 3, 1, 3, 3, 1, −3, −1, −1,3}; and S6={1, 3, −3, −3, 3, −3, 1, −1,−1, 3, −1, −3}.
 43. A userequipment transmitter for use with a cellular communication system,comprising: a reference signal unit configured to provide a referencesequence for an uplink reference signal corresponding to a one or tworesource block allocation of the user equipment by selecting onesequence from thirty sequences stored in a memory of the user equipment;a sequence generation unit configured to generate a reference sequencefor the uplink reference signal corresponding to a resource blockallocation that is greater than two; and a transmit unit configured totransmit the uplink reference signal.
 44. The user equipment transmitteras recited in claim 43 wherein the reference sequences stored in thememory are QPSK sequences.
 45. The user equipment transmitter as recitedin claim 43 wherein the reference sequence generated is a Zadoff-Chusequence.